LiDAR is a new type of sensor used for gait recognition. Previous LiDAR-based state-of-the-art methods mostly exploit gait features from the depth maps generated by projecting point clouds in a 3D-to-2D manner, rather than directly using the raw 3D point data. However, these projection-based methods require an additional preprocessing step, which obstructs the universality of the method among different types of LiDARs. On the other hand, while existing point-based methods have achieved promising results in 3D object recognition, they have underperformed in 3D gait recognition, indicating the presence of a domain gap between coarse-grained 3D object classification and fine-grained 3D pedestrians recognition. By analyzing the success achieved by camera-based methods, we perceive that point-based gait recognition fails mainly because of neglecting to capture local representation. To address this issue, we propose an end-to-end 3D gait recognition framework named PointGait, which can directly capture informative gait features from point cloud data. Specifically, PointGait is a multi-stream model consisting of a Global and Local Gait Feature Extractor to extract holistic and fine-grained spatial features. Besides, a Personalized Motion Extractor is introduced to capture inter-frame motion features. Our experimental results on a LiDAR gait dataset, SUSTech1K, outperform all popular point-based methods, demonstrating the effectiveness and potential of our approach. In conclusion, the proposed PointGait promotes the development of point-based gait recognition by highlighting the importance of incorporating fine-grained spatiotemporal information.